Despite his excellent power numbers in the minors, Bream demonstrated mostly gap power in the majors (resulting in lots of doubles), and he was known for above-average defense at first base. The Dodgers expected him to compete with Greg Brock for the first base job, as Brock had performed below expectations after longtime starter Steve Garvey left to sign with the San Diego Padres. But Bream failed to hit for the Dodgers in multiple opportunities from 1983-85.

The Dodgers finally gave up on Bream late in the 1985 season and traded him along with Cecil Espy and R.J. Reynolds to the Pittsburgh Pirates for Bill Madlock, who the Dodgers wanted as they pursued the NL West title. It was in Pittsburgh where Bream finally had a chance to play every day. In 1986 he set an MLB record with 166 assists at first base. Bream's best season at the plate in Pittsburgh was also 1986 when he batted .268 with 16 home runs and 77 runs batted in.

Following the 1990 season, Bream became a free agent and signed with the Atlanta Braves. He suffered through injuries in Atlanta, which limited his playing time. However, he did play in two World Series, in 1991 and 1992. After a poor start in 1993, the Braves acquired Fred McGriff from the San Diego Padres to play first base and Bream was relegated to pinch-hitting for the rest of the season.

The most famous moment of Bream's career came in Game 7 of the 1992 National League Championship Series. Bream was the Atlanta first baseman, and the Braves were playing his old team, the Pittsburgh Pirates, in the NLCS.

The Pirates carried a 2-0 lead into the bottom of the ninth inning under the pitching of their ace, Doug Drabek, needing just three outs to make the World Series. However, Drabek gave up a leadoff double to Terry Pendleton, then allowed another runner (David Justice) on an infield error by second baseman José Lind. After Drabek walked Bream to load the bases, Pirates manager Jim Leyland pulled him out of the game. Reliever Stan Belinda replaced him on the mound, and managed to get two outs, despite giving up a run on a sacrifice fly by Ron Gant. Then, Braves third-string catcher Francisco Cabrera belted a single to left field, and Justice scored easily to tie the game. Pirates left fielder and eventual National League MVPBarry Bonds fielded the ball as Bream ran toward home plate. Bonds's throw arrived first, but it was slightly offline and bounced on its way towards the first-base line. As soon as catcher Mike LaValliere received the ball, he desperately lunged toward the plate to tag Bream out, but Bream was able to slide just underneath the tag to score the winning run and send the Braves to the World Series for the second consecutive year.

Following the 1993 season, Bream signed with the Houston Astros and served as a backup to Jeff Bagwell, and continued his success as a pinch-hitter. He hit .344 in limited play, and retired during the baseball strike.

Bream retired to the northern suburbs of Pittsburgh, Pennsylvania where he lives with his wife Michele.[2] The couple have four children.[2] He is currently a motivational speaker and served as the hitting coach for the State College Spikes in 2008.[3] Bream serves as the spokesman for Christian Sports International (CSI,) a 501(c)(3) faith based charity based in Pittsburgh. His second child Tyler attended Liberty University on a baseball scholarship and was drafted by the Arizona Diamondbacks in the 42nd round (1264th overall) in 2011.[4]

On November 13, 2015, it was announced that Bream would take a job as Corporate Chaplain for PGT Trucking, which is located just outside Pittsburgh, Pennsylvania.[5]